I know there are several ways, but what do you recommend as the best way to add fonts that won't break the theme?

I did, however when i follow the directions and add the code snippet, my custom TypeKit font is not showing up. See the attached screenshot. It should be Proxima Nova in there, which is my TypeKit font.

Thanks, might be good to update that help section denoting that's what's needed to make it work as it's a bit unclear. 

I'm also trying to get the font to show up inside a page. Is that possible? I attached a screenshot to show that Proxima is not showing up in the font list.